Let $F$ be a relatively closed subset of a Euclidean domain $\Omega$. We investigate when solutions $u$ to certain elliptic equations on $\Omega\setminus F$ are restrictions of solutions on all of $\Omega$. Specifically, we show that if $\partial F$ is not too large, and $u$ has a suitable decay rate near $F$, then $u$ can be so extended.
@article{119059,
author = {Stephen M. Buckley and Pekka Koskela},
title = {On the fusion problem for degenerate elliptic equations II},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {40},
year = {1999},
pages = {1-6},
zbl = {1060.35511},
mrnumber = {1715198},
language = {en},
url = {http://dml.mathdoc.fr/item/119059}
}
Buckley, Stephen M.; Koskela, Pekka. On the fusion problem for degenerate elliptic equations II. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 1-6. http://gdmltest.u-ga.fr/item/119059/
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